Root mean square error (RMSE; common colour scale on top), for the analysis described in Sect. 3.2, using the shock models of Aoyama et al. (2018, 2020, 2021). The two input parameters are the pre-shock gas velocity v₀ and the number density of hydrogen nuclei n₀. The smaller the RMSE is, the better the fit with the one-sigma regions (RMSE ≲ 1; Eq. (3)) in blue. Upper panels: H5₃₃, H6, and H7₂₃. Lower panels: H7₂₄, H8, and H9. The dashed and dotted horizontal lines indicate n₀ = 10¹³ cm⁻³ and n₀ = 10¹¹ cm⁻³, respectively. At higher densities (n₀ ≳ 10¹³ cm⁻³), both the NC and BC of the data are reproduced by the model, while the lower density only accurately reproduces the NC. The lack of constraints on the parameters from the H9 line is likely due to the low line-S/N.